62514
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Writing and Solving Equations in Two Variables

Question 62514 • WV-Algebra I CR

An isosceles triangle has two sides of equal length, a, and a base, b. The perimeter of the triangle is 15.7 inches, so the equation to solve is 2a + b = 15.7.If we recall that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side, which lengths make sense for possible values of b? Select two options.–2 in.0 in.0.5 in.2 in.7.9 in.

Answer
A
–2 in.
B
0 in.
C
0.5 in.
D
2 in.
E
7.9 in.

Explanation

The equal sides have total length 15.7 − b, so the triangle inequality requires 15.7 − b > b. Solving gives b < 7.85, and a side length must also be positive, so b > 0. Thus 0.5 in. and 2 in. are possible; 7.9 in. is too long, and −2 in. and 0 in. cannot be side lengths.

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